Probability worksheet with answers

Free printable Probability worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xp(x)100.25200.2300.240?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.25, 0.2, 0.2, ?
P(X = 40) =
2.Easy
sum ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
3.Medium
n = 11k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 11? The order does not matter.

n = 11k = 2
N =
4.Medium
n = 13k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 13? The order does not matter.

n = 13k = 5
N =
5.Hard
n = 5, p = 0.4: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 5p = 0.4
P =
6.Hard
xp(x)00.3510.3520.3μ

X has the distribution shown, and Y = −2X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.35, 0.3Y = −2X + 20
σY =

Answer key

  1. 1. P(X = 40) = 0.35
  2. 2. P = 0.1667
  3. 3. N = 55
  4. 4. N = 1287
  5. 5. P = 0.337
  6. 6. σY = 1.609

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